I can‘t assign three materials and UV maps to multiple objects
The comment that moonboots gave is the best answer if all your cans are exactly the same. However, if the constraints and shape keys on them are differing from each other, those individual informations would be lost. So this might help as a workaround (if they still share the same mesh):

Select all cans so that the one with the correct UVs is the active one. Then Ctrl+L &gt; Make Links &gt; Transfer UV Maps. This way they have all the same UV maps.
Now you have to link all materials to the other cans. Ctrl+L &gt; Make Links &gt; Materials. Now all materials, no matter how many, are put on all the other cans.
The problem with this is, since you can copy materials to different objects that not necessarily share the same geometry, Blender doesn't transfer the information to which faces they are assigned. That's what you have to do manually.

It's still a lot of work I guess, but maybe less than having to do all constraints, shape keys, rotations, etc. over again. If someone knows how to copy face assignments for materials, please edit this answer.
A different solution would be: combine all three different materials in one material and separate them by masks and UVs, then all cans would only share one material with one UV map and there was no need for re-assigning faces.